基于有限差分法的多介质高温作业服设计的优化数学模型  

An Optimization Mathematical Model for Design of Multi-Medium High Temperature Operation Suit Based on Finite Difference Method

作　　者：孙宝宸 吴宜均 

机构地区：[1]天津师范大学,数学科学学院,天津

出　　处：《应用数学进展》2019年第2期334-349,共16页Advances in Applied Mathematics

摘　　要：本文主要研究一种典型高温作业专用服的一维温度分布和厚度优化。首先,运用有限差分法对连续的传热模型进行离散化,利用有约束非线性规划对未定参数进行估计,仿真75摄氏度高温环境下服装内部温度分布。其次,通过减少约束条件简化单目标规划问题,利用Fibonacci法、黄金分割法、二分法和二次插值法进行求解,最优值为17.6毫米。最后,本文提出一种有效缩短区间长度求解可行边界点的算法,采用简单完全分层序列法对多目标规划模型进行求解,求得II、IV层最优厚度分别为19.2毫米与6.4毫米。This paper mainly studies the one-dimensional temperature distribution and thickness optimiza-tion of a typical high temperature operation special suit. Firstly, the finite difference method is used to discretize the continuous heat transfer model, and the undetermined parameters are estimated by using the constrained nonlinear programming, and the internal temperature distribution of the garment in 75 degrees Celsius high temperature environment is simulated. Secondly, by reducing the constraint conditions to simplify the single-objective planning problem, the optimal value is 17.6 mm by using the Fibonacci method, the Golden section method, the dichotomy method and the two-interpolation method. Finally, an algorithm for effectively shortening the interval length to solve the feasible boundary points is proposed, and a simple complete layered sequence method is used to solve the multi-objective programming model, and the optimal thickness of the II and IV layers is 19.2 mm and 6.4 mm.

关 键 词：非稳态热传导模型 多目标规划 约束非线性规划 有限差分 简单完全分层序列法 

分 类 号：F2[经济管理—国民经济]